Question

How do you simplify $\dfrac{{\ln 1}}{2}$ ?

Answer 1

Hint: ln is the natural logarithm and it is log to the base “e”. First of all we will find the value of $\ln 1$ and then place the value in the given expression and then simplify the expression for the resultant value.

Complete step-by-step answer:
First of all find the value of $\ln 1$
We know that the value of $\ln 1 = 0$
Place the above value in the given expression.
$\dfrac{{\ln 1}}{2} = \dfrac{0}{2}$
Zero upon anything is always equal to zero.
$\dfrac{{\ln 1}}{2} = 0$
This is the required solution.

Additional Information:
In other words, the logarithm is the power to which the number must be raised in order to get some other. Always remember the standard properties of the logarithm.... Product rule, quotient rule and the power rule. The basic logarithm properties are most important and the solution solely depends on it, so remember and understand its application properly. Be good in multiples and know its concepts and apply them accordingly.
Also refer to the below properties and rules of the logarithm.
Product rule: ${\log _a}xy = {\log _a}x + {\log _a}y$
Quotient rule: ${\log _a}\dfrac{x}{y} = {\log _a}x - {\log _a}y$
Power rule: ${\log _a}{x^n} = n{\log _a}x$
 Base rule:${\log _a}a = 1$
Change of base rule: ${\log _a}M = \dfrac{{\log M}}{{\log N}}$

Note: Know the difference between ln and log and apply its properties accordingly. Logarithms are the ways to figure out which exponents we need to multiply into the specific number. Log is defined for the base $10$ and ln is denoted for the base e. “e” is an irrational and transcendental number which can be expressed as $e = 2.71828$. You can convert ln to log by using the relation such as
$\ln (x) = \log x \div \log (2.71828)$